Can you apply an action to an armature that has more bones than the one that created the action?
The toe bone shouldn't be a problem, but an extra spine bone might be, as it will have children that are animated by the armature. Because of this it is likely that the transferred animation may never look the same.

To fix this I'd suggest adding an extra control bone to the mixamo armature named after one of the bvh bones and constrain two of the spine bones (the dupilicate and another) to move based on its rotation. A picture of the two armatures would make this easier to explain. 

You may want to check that the bone rolls on each bone in edit mode match between the two armatures.